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The phrase "about the proof" is correct and usable in written English.
It can be used when discussing a topic related to evidence, verification, or a mathematical or logical argument.
Example: "The discussion was primarily about the proof of the theorem presented in the lecture."
Alternatives: "regarding the proof" or "concerning the proof".
Exact(13)
Many of you have also asked for some clarification about the proof of Cantor's theorem.
With a typed statement about the proof of Alfred William Hunt's will.
Scott Book, Bob's son, looked on, approvingly, from across the table, as Huckabee reminisced about his mother's penny collection, back in Arkansas, and about the proof sets of quarters that he and his sister received each Christmas.
Questioned in a February pretrial hearing about the proof of child trafficking, one investigator responded that "the adoption process consists of searching for children who are good-looking and well-behaved, and who have hereditary features that are similar to those of the parents," according to a translation of the court's Arabic transcript.
DB: Using my influence to promote my brand was really about the proof in the pudding.
About the proof of Lemma 2.2, we can see that formula (2.9) is vital.
Similar(47)
And [13, 15] give more details about the proofs of a few common aggregation functions.
The cool thing about the proofs, is that they can be embedded into any web page, so ProofHQ documents can can also be integrated into project management applications like Basecamp or Huddle.
Another claim neo-Confederates make is that the Civil War was not about slavery, the "proof" being that only 0.00000004% of Confederates ever even thought about owning slaves, and never mistreated any.
Moving his wife and son to safety, he goes about getting the proof he needs.
As he spoke, just about all the proof anyone needed was taking place over his left shoulder across Garden Street.
More suggestions(16)
about the validation
about the guide
about the demonstration
about the justification
about the probation
about the testing
about the documentation
about the verification
about the leadership
about the evidentiary
about the rationale
about the radio
about the proposal
about the individual
about the book
about the money
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com